Permutations question

[ahem]

Hello: I am on a museum exhibit-development team and have a question about an intro-level genetics demo we're working on. In the demo, we'll show two parents and a small sample of the genes they each pass on to their offspring. Each parent's "population" of chromosomes will consist of 7 genes (e.g., eye color, hair color, etc), and each gene can take on one of two settings, which allows visitors to experiment by seeing how different combinations of genes create offspring with a wide range of traits. Obviously, we are greatly simplifying the real situation by both reducing each parent's chromosome set to 7 and by ignoring various complexities, like some traits being sex-linked, etc. My question is: With two sets of 7 wheels (14 total), each of which can take on two settings, what is the correct formula to use for determining the total possible number of distinct outcomes? 14 choose 2?
Thank you!

 

[hlsmith]

Great stuff. Yeah I was going to harp on the complexities of genomics, but thankfully you had a disclaimer. It would be ideal if you passed the disclaimer along to the patrons. Also, of interest would be that if we uncoiled our DNA it would stretch to like Jupiter three times and if you spoke each amino acid name in our genome it would take like a century to same them all.

Of note, permutation is when the order of the 'genes' in the pair matters and combination is when they don't. So if AG is different than GA you are talking permutations.

So, Gene #1 for eye color can be G or B in mom and H or B in dad, how many combinations/permutations are possible? Now Gene #2 for hair color can be R or B in mom and B or B in dad given his parent were both B. Or should we just imagine each gene could be 0 or 1? Can you provide a little dataframe of what you are proposing, please.